laplacetransform f(x)=xe^{2x}sin(6x)

Lösung

laplace transformation

f (x) = x e^{2 x} sin (6 x)

\frac{6 ( 2 s - 4 )}{( s ^{2} - 4 s + 40 ) ^{2}}

Schritte zur Lösung

L {e^{2 x} x sin (6 x)}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

x e^{2 x} sin (6 x) : f (x) = e^{2 x} sin (6 x), k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{2 x} sin (6 x)})

L {e^{2 x} sin (6 x)} : \frac{6}{( s - 2 ) ^{2} + 36}

\frac{d}{d s} (\frac{6}{( s - 2 ) ^{2} + 36}) = - \frac{6 ( 2 s - 4 )}{( s ^{2} - 4 s + 40 ) ^{2}}

= (- 1)^{1} (- \frac{6 ( 2 s - 4 )}{( s ^{2} - 4 s + 40 ) ^{2}})

= \frac{6 ( 2 s - 4 )}{( s ^{2} - 4 s + 40 ) ^{2}}

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